Probability of occurrence
0.4621%
(4 heads out of 20 tosses)
Formula
Step 1: Desired heads
Step 2: Binomial coefficient
Step 3: Probability
This is a simple visualizer to show you how the probability of getting a certain % of your tosses (say 50%) as heads (or tails). For instance, the probability of getting half your tosses as H or T never goes over, well, 50%. The fewer the number of tosses, the higher the probability of any one single outcome.
By symmetry, heads and tails are equally likely. So P(heads > 50%) = P(tails > 50%). Since these two events can't both happen at once (you can't have more than half heads AND more than half tails), each probability is at most 50%.
Here's a fun paradox: getting exactly 50% heads is the single most likely outcome - yet its probability shrinks toward zero as you flip more coins. For 100 flips, landing exactly 50 heads has only about an 8% chance.
The "most likely" outcome can still be quite unlikely. Each additional flip spreads the probability across more possible outcomes.